论文标题
两个真实石墨烯和热力学之间Casimir效应的量子场理论描述
Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics
论文作者
论文摘要
Casimir自由能的分析渐近表达式和具有非零能隙$δ$和化学势$ $ $的两个平行石墨烯片的熵是在任意低温下得出的。石墨烯在Matsubara公式的热量子场理论的框架中描述了（2+1）维时时间。在条件下发现不同的渐近表达式，$δ>2μ$，$δ=2μ$，以及$Δ<2μ$，同时考虑了由于对Matsubara频率的求和而引起的隐式温度依赖性，又要考虑到由偏振量对温度作为参数的偏振量的依赖而引起的显式温度。结果表明，对于$δ>2μ$和$Δ<2μ$，Casimir熵满足了热力学的第三定律（Nernst Heats Heat Theorem），而对于$δ=2μ$，此基本要求违反了。在金属和介电体之间卡西米尔效应的热力学特性的背景下，考虑了发现的异常的物理含义。
The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $Δ$ and chemical potential $μ$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2+1)-dimensional space-time. Different asymptotic expressions are found under the conditions $Δ>2μ$, $Δ=2μ$, and $Δ<2μ$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both $Δ>2μ$ and $Δ<2μ$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $Δ=2μ$ this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.
